TM35 can be bought at the celadon game corner.
You can "purchase" a flamethrower TM in the game corner coin-tradey place.
Umm... the question needs to be a little more specific. (Example: where can I find Flamethrower?).
It learns Flamethrower at level 34.
It Is In The Game Corner.
TM35
Yes, by TM35.
You can trade a Pokemon that is holding the TM from diamond to soulsilver or pearl or platinum or you can migrate a Pokemon holding the TM from ruby, sapphire or emerald or firered or leafgreen.
inside of Fuego Ironworks(but you have to have HM3)
Yes. I cannot remember, but I think it is TM35.
Flamethrower is TM 35, and it can be obtained by buying it in the Game Corner Shop in Celadon City for 4000 coins.
It's up to you. I taught mine psychic, recover, swift, and flamethrower. I almost beat the elite 4 with this Pokemon alone.
I don't think there is a TM for it but you can get a Charizard, it will learn flamethrower, then breed that Pokemon with a Ditto, then that charmander should know flamethrower.